Catamaran Wave Interference

Does anyone have a summary or cliff notes version of the linked whitepaper?

I'd like to plug in my catamaran's info into it and see if I can understand things a bit.

It is fairly condensed already, but not sure if I build an excel spreadsheet if I will get it right or understand the outputs..

The designer did provide hydrostatics, not sure if those include these outputs; certainly some inputs are there.

For example, is the distance between the two cat hulls center to center or minimum between waterlines on each hull, etc.

In the absence of a reply, I may have a go at excel and link it here.

Thanks.

http://www.iwwwfb.org/Abstracts/iwwwfb30/iwwwfb30_64.pdf

 

FG- Thanks for the link. I still have to digest it.

Distance between the hulls can be from center to center or between hulls depending on the author. This is the lateral offset. Then there is also the longitudinal offset where one hull leads the other such as in Proa.

In the Principles of Naval Architecture book, it is defined as distance between the two hulls. Beneficial distances is when the wave cancels each other out. Note that interference benefits can only be had at certain Froude numbers.

 

Here is the enlarged view

 

I will try to build an excel sheet, but still lacking a basic understanding...

 

Can't help you with the math, but the interference depends upon both the distance between centerline of the hulls, and the width of each hull.
A silly illustration is a 4' cl to cl width for 2 boats, but boat 1 has a hull width of 6" and hull 2 has a width of 2'.

I had a rowing catamaran of 6' between centerlines and a 18" hull width. Horrible interference.
Moved the centerlines to 8' with the same hull width (same hulls) and there was an instant big improvement. Minimal visually seen interference.
FYI, the boat length was 11'.

The reason this came up was that my wifes 11' long, 6' between CL and 6" wide hull easily out rowed me and I couldn't stand it!
The reason for the difference in hulls was/ is that my wife weights 1/2 of what I did/do.

 

Thanks for the linked paper, I will look at it.
At first, as regard a monohull at high speed > 0,5, it seems they refer, among other considerations, to the Kelvin angle reduction (their figures 4a, 4b, 4c). Here is a paper on the same issue, where authors Rabaud & Moisy shows pictures and angle measurements in their Fig. 1 and 2 , and propose a theory inc. a simple asymptotic for the Kelvin angle reduction (Formula (4), also shows on Fig. 2) and a simulation with their theory in Fig. 5a to 5d : from 19,47° at small Fr, the angle falls to 18,9° at Fr 0,5, 15,9° at Fr 1, 5,8° at Fr 2 and 2,9° at Fr 4 . All that because of course, this angle reduction is of first importance to further deal with wave interference in catamaran mode at high speed.
http://www.fast.u-psud.fr/~moisy/papers/2013_rabaud_prl.pdf

I am also trying to do a speadsheet application adressing the residuary drag issue of high speed sailing catamaran, I underline sailing because that means a heeled catamaran configuration leading to two very different hulls (even with few degrees of angle) : the leeward one and the windward one, of different Lw, Bw, displacement, draft Tc, transom immersion (or not), and moreover (as Lw is different) functioning at different Froude. Within another thread (here below reminded), thanks to reports on model test series provided by members, I try to initiate a uniformed adimensional approach to estimate such resisduary drag, inc. some empirical considerations to deal with the heeled cata mode (by absence of specific tests results), with in mind to digitalise all that for a VPP spreadsheet application useful to an early stage project level. Here is my progress on that with numerical examples, presently without link with theoritical academic consideration as above, just based on experimental results.
Calculating friction resistance, drag coefficient? https://www.boatdesign.net/threads/calculating-friction-resistance-drag-coefficient.62553/

 

FG- The article says the spacing to length ratio is center to center distance. Unless you are doing the Excel spreadsheet for academic study, why don't you try Michlet by Leo Lazauskas. His program is dowloadable here in the forum. It is difficult to use but it will take you more time to develop the spreadsheet and validate it. The article available from his site provides also lots of graphs and optimum hull spacing.

I made a program years ago but is dated. What is the speed you are running the cat? Also the Lwl, beam, displacement. I can run it and see if you are in the beneficial range. The s/L ratio is only beneficial at certain Taylor's/Froude number as shown in the graph. It is most beneficial if you are running at Fn 0.33 at s/L of 0.3. At certain ratio, the interference effect only deducts from the performance.

 

LWL --> 9.504 M, or 9.656 with engine extension
Center line to Centerline of Hulls --> 3.807M
Hull Width at Waterline --> 0.841M (edited was originally 0.61 <---wrong)
freshwater displacement --> 1.976 M^3, !per hull!
CCP --> .665

Speeds of cat 0 -> 26mph; perhaps a bit higher, 10mph typical for a Froude number of 0.46 if my math is correct.

The hull is a knife forward and flattens out aft, so it will lift some at speed

Thanks. This stuff is a little beyond my reach alone. I want to understand a couple things. I wanted to better understand where I benefit from interference and where I lose (at what speeds).

This cat is demountable, so you only see the starboard hull.

 

Have you also an estimation of the hull body draft Tc (at displacement 1,976 m3) ? And also the wetted surface in this same displacement (if you have the drawing of this hull) ? I could then test my approach et with various S/L.

 

Fair body draft is 0.451M and wsa is 10.674 M^2 (per hull I believe)

 

Ok, many thanks, and yes Sw is very likely for one hull, Sw/D^(2/3) = 6,78 is in the order of magnitude (the numerical 16 m cata I use as reference in Gene-Hull has Sw/D^(2/3) = 6,57 per hull)
I presume we are considering a motor-yacht catamaran, no need to consider heel angle, just the upright mode ?
Let's check at first the ratios involved in the approach and comparison with the domain of validity due to the model test series :
** Lw/Bw = 11,3 / 7 to 18
** Bw/Tc = 2,03 / 1,5 to 2,5
** Lw/D^(1/3) = 7,57 / 6,5 to 12,5
** S/Lw = 0,40 / 0,3 to 0,5 (S = transversal space between the 2 hulls axis)
** Cb = 0,55 / 0,35 to 0,55 (ok for the slender monohull drag, but for the S/Lw influence specifically, the experiments were done only with a serie of models sharing the same Cb = 0,4 and Cp = 0,69 >>> importance ?)
** Speed 0 to 26 mph = Froude 0 to 1,2 / valid up to Fr ~ 0,9 - 1,0 For Fr > ~ 0,9 -1,0 , not only we are at the limit of the model test results but also the limit beyond which the dynamic lift can play a major role even with such high L/B hull, a role dependent of the hull shape (deadrise angle, …) and not captured by the above ratios.
So I will do drag estimation (residuary and friction) and S/Lw influence on this basis (asap in a few days …).

 

Yes, motor vessel.

Yes, the wsa is single for sure on further reflection.

Here is a bottom picture. Beaching keel without sacrificial bit. It is 22" wide and flat at stern with a tad bit of rocker. The sacrificial portion of the beaching keel is a piece of wood that follows the keel lines and ends at about a 2" flat.

The photo is deceptive. The stern is like 9' from the end of the keel or so.

 

My Michlet would no longer run in my 64bit computer but it was easier than I thought on how to explain it using the graph.

You have a boat whose spacing to length ratio is 0.4 Looking at the graph and plotting the various speed and following the wiggly lines of 0.4, it is easy to see where the beneficial ratio is. It is beneficial when the graph says negative where the divergent wave generated by each hull cancels each other. Thus at Fn 0.24 and at 0.33. All above is detrimental. Since you will be running up to 26 mph (Fn 1.21) I have to use the extended graph on the right. At Fn 0.75 to 0.8 the complex curves forms a singularity. This means the effects of wave interference is small and can be neglected. Nothing to worry about.

The left graph follows the Kevin's angle while the in the right graph I presume the extension follows the Mach angle. This is in the paper provided in the link by Dolfiman. My book, Principles of NA also says "interference effects are small at speeds starting at Fn 0.8".

 

In a nut shell.
You need to make the spacing ratio(hull CL to hull CL) S/L as large as possible.
But an S/L of 0.20min for resistance to eliminate any adverse effects of blockage.. Increase the S/L improves with increasing S/L. Downside is that the GM becomes higher and thus the motions are sharp and stiff, not pleasant.
A higher L/D ratio impoves the situation.
If your figures are correct, Lwl = 9.50m and Displacement = 2.0 tonne, then you L/D ratio is 7.5, which is on the more positive side.

Thus I would say if you aim for around S/L = 0.25-ish as a min, you will be ok.

 

The S/L is 0.394.

All my figures are correct. The boat is very close to structurally complete. I am just trying to understand the numbers a bit better.

Sorry AH, but you tend to talk over me a bit. I don't know what you mean by the GM.... What do you mean by higher GM and sharp and stiff unpleasant motion?